MATH 294: MATHEMATICS OF FINANCE (WINTER 1999)
Professor R. J. Williams
Time: M 4.40--6.10 p.m., W 5.10--6.10 p.m.
Place: AP&M 7421
Office Hours: M & W, 3--4 pm, AP&M 6121.
This course is an introduction to the mathematics of financial models.
The aim is to provide students with an introduction to some basic
models of finance and the associated mathematical machinery.
The course will begin with the development of the basic ideas of hedging and
pricing by arbitrage
in the discrete time setting of binomial tree models.
Key probabilistic concepts of conditional
expectation, martingale, change of measure, and representation,
will all be introduced first in this
simple framework as a bridge to the continuous model setting.
Mathematical fundamentals for the development and analysis of continous time
models will be covered, including Brownian motion, stochastic calculus, change
of measure, martingale representation theorem. These will then be combined
to develop the Black-Scholes option pricing formula.
Pricing and hedging for European and American call
options will be discussed.
Attention will then turn to models of the interest rate market.
Various models will be discussed, including the
and Cox-Ingersoll-Ross models.
As time permits, more general
models and extensions will be described.
These will complement the theoretical material presented in the course.
Students may wish to enrol in
Math 161 in the Fall of 1998, which will include an Introduction to Mathematica.
Mathematics of Financial Markets, R. J. Elliott
and P. E. Kopp, Springer, 1998. This book is now available in the
Investment Science, David G. Luenberger, Oxford University Press, 1998.
Financial Economics, H. H. Panjer (ed.),
Actuarial Foundation, Schaumburg, Illinois, 1998.
Options, Futures and other Derivative Securities, J. Hull, Prentice Hall, 1993.
Background in economics/finance:
Mathematics of Finance: Stochastic Approaches
Financial calculus, Martin Baxter and Andrew Rennie, Cambridge University Press,
Introduction to Stochastic Calculus Applied
to Finance, D. Lamberton and B. Lapeyre,
Chapman and Hall, 1996.
An Introduction to the Mathematics of Financial Derivatives,
Salih N. Neftci, Academic Press, 1996.
Steven Shreve's Lectures on Stochastic Calculus and
Finance, Prepared by P. Chalasani and S. Jha.
Mathematics of Finance: PDE Approach
The Mathematics of Financial Derivatives: A student introduction, Paul Wilmott, et al., Cambridge
University Press, 1995.
Mathematics of Finance: more advanced stochastic
Martingale methods in financial modelling,
M. Musiela and M. Rutkowski, Springer, 1998.
Methods of mathematical finance, I. Karatzas
and S. Shreve, Springer, 1998.
MATHEMATICAL FINANCE TALKS AT UCSD Mathematical Finance talk
by R. J. Elliott at UCSD
Probability Seminar talk by Bernt Oksendal:
"A short introduction to Malliavin calculus and its application to finance",
Thursday, February 25, 1999, 10.10am, AP&M 6218.
For Oksendal's notes on Malliavin calculus, click here.
Professor Harry Markowitz, Leverage and Growth: with implications
Thursday, March 11, 1999, Price Center Theater, 5 p.m.
LINKS TO RELATED WEB SITES (under construction):
Please direct any questions to
Professor Ruth J. Williams, email: